First of all this Set up is only ONE design... and the Pictures are given to show design ONLY...
My thoughts are only my opinion based on using various different bodygrip traps for over 30 years... however they are my firm beliefs in the Benefits of using the Belisle line of traps.
Side of Coon box made for Belisle 220 or 160... note long setback cut, and extended top... this does not lower the Coon catchs, only prevents dogs from getting to the trap. These notches are a little wide, but the depth is just right.
Front Shot showing the Belisle Safety hooks staying where you put them... Huge benefit!
Jaw corners that don't allow Spring loops to go around them.
The backside of the Dog is flat, this allows for the jaws to close very tightly, other dogs keep the jaws apart almost 3/16th of an inch or more on some brands.
The Belisle Safety hooks in my mind are their best benefit... When setting a trap, having a hook that does not swing freely and stays where you want it is awesome, plus when making the set they allow you to complete the Make, before releasing the safetys, and when the Trap fires there is zero chance that the hooks can (as they sometimes do) swing catching the spring... and not allowing the trap to close 100%
As I said above, these Pictures are for example and my thoughts are just my opinion.